My wife has had the same problem and it is SIBO (Small Intestinal Bacterial Overgrowth). She has had her gallbladder removed but the problem with burping is still around, she has figured out that limiting what she eats helps, but nothing seems to stop the burping altogether.
Start with asking your doc to run an H. pylori test on you. People who have this bacteria that's correlated with acid reflux problems often report a lot of burping - even when they don't have blatant 'acid' symtpoms like 'heartburn.'
Burpiing can also be the result of gallbladder issues.
My dad has this problem too. He burps when he lets himself get too hungry, then he burps while he is eating. He can't sleep because he starts burping, be actually went to the ER a few weeks ago because he was in so much pain from the burping. His Primary Care Physician does not think it is acid reflux, I think she is definitely wrong.
I am going to buy him some bed lifters and see if that helps, I don't think he has had a solid 8 hours of sleep in several years, I can't imagine how this is effecting the rest of his body, he is 71, not over weight, and has never smoked or drank. And since a triple bypass in '92 has maintained a pretty healthy diet.